Abstract. This paper concerns a numerical stabilization method for free-surface ice flow called the free-surface stabilization algorithm (FSSA). In the current study, the FSSA is implemented into the numerical ice-flow software Elmer/Ice and tested on synthetic two-dimensional (2D) glaciers, as well as on the real-world glacier of Midtre Lovénbreen, Svalbard. For the synthetic 2D cases it is found that the FSSA method increases the largest stable time-step size at least by a factor of ten for the case of a gently sloping ice surface (3°), and by at least a factor of five for cases of moderately to steeply inclined surfaces (6° to 12°) . Furthermore, the FSSA method increases the overall accuracy for all surface slopes. The largest stable time-step size is found to be smallest for the case of a low sloping surface, despite having overall smaller velocities. For Midtre Lovénbreen the FSSA method doubles the largest stable time-step size, however, the accuracy is in this case slightly lowered in the deeper parts of the glacier, while it increases near edges. The implication is that the non-FSSA method might be more accurate at predicting glacier thinning, while the FSSA method is more suitable for predicting future glacier extent. A possible application of the larger time-step sizes allowed for by the FSSA is for spin-up simulations, where relatively fast changing climate data can be incorporated on short time scales, while the slowly changing velocity field is updated over larger time scales.
<p class="p1">Ice flow models often suffer from numerical instabilities that restricts time-step sizes. For higher-order models this constitutes a severe bottleneck. We present a method for increasing the largest stable time step in full Stokes models, allowing for a significant speed-up of simulations.<span class="Apple-converted-space">&#160; </span>This type of stabilisation was originally developed for mantle-convection simulations and is here extended to ice flow problems. The method is mimicking an implicit solver but the computational cost per time step is nearly as low as for an explicit solver. As it only consists of adding a stabilisation term to the gravitational force in the full Stokes equations, it is very easy to implement. We test the method using both Elmer/Ice and FEniCS on artificial glaciers with varying bedrock roughness, slip rate and surface inclination, as well as on a real world case.</p>
<p>In order to understand the rate at which an ice sheet is losing mass one has to consider its dynamics. Ice is a very slow moving, highly viscous, non-newtonian fluid and as such is most accurately described by the full Stokes equation. Time dependence is taken into account by coupling the Stokes equation to the so called free surface equation, which describes how the free surface boundary of the ice sheet is advected due to the Stokes velocity field.</p><p>A problem with this system is that it is numerically quite unstable and has a very strict time step constraint, where very small time steps are needed in order to have a stable solver. This constitutes a severe limitation for making long term predictions as the expensive nonlinear Stokes equation has to be solved in each time step.</p><p>By adding an additional term to the weak form of the Stokes equation we achieve stability for time steps 10-20 times larger than without stabilization. This stabilization technique is straightforward to implement into existing code and does not result in significantly larger computation times or memory usage.</p>
Numerical models for predicting future ice-mass loss of the Antarctic and Greenland ice sheet requires accurately representing their dynamics. Unfortunately, ice-sheet models suffer from a very strict timestep size constraint, which for higher-order models constitutes a severe bottleneck since in each time step a nonlinear and computationally demanding system of equations has to be solved.In this study, stable time-step sizes are increased for a full-Stokes model by implementing a so-called free-surface stabilization algorithm (FSSA). Previously this stabilization has been used successfully in mantle-convection simulations where a similar, but linear, viscous-flow problem is solved.By numerical investigation it is demonstrated that instabilities on the very thin domains required for ice-sheet modeling behave differently than on the equal-aspect-ratio domains the stabilization has previously been used on. Despite this, and despite the nonlinearity of the problem, it is shown that it is possible to adapt FSSA to work on idealized ice-sheet domains and increase stable time-step sizes by at least one order of magnitude. The FSSA presented is deemed accurate, efficient and straightforward to implement into existing ice-sheet solvers.
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